Search results for “filtered colimits”

Fun example: empty colimit does not commute with empty limit

2026NotesBogdan Zavyalov

Why the definition of a filtered category insists on non-emptiness: the empty colimit fails to commute with the empty limit, and that is the only failure.

LomonosovMSU at SemEval-2024 Task 4: Comparing LLMs and embedder models to identifying propaganda techniques in the content of memes in English for subtasks No1, No2a, and No2b

2024Conference paperGleb Skiba, Mikhail Pukemo, Dmitry Melikhov, Konstantin Vorontsov

This paper presents the solution of the LomonosovMSU team for the SemEval-2024 Task 4 "Multilingual Detection of Persuasion Techniques in Memes" competition for the English language task.During the task solving process, generative and BERT-like (training classifiers on top of embedder models) approaches were tested for subtask №1, as well as an BERT-like approach on top of multimodal embedder models for subtasks №2a/№2b.The models were trained using datasets provided by the competition organizers, enriched with filtered datasets from previous SemEval competitions.The following results were achieved: 18th place for subtask №1, 9th place for subtask №2a, and 11th place for subtask №2b.The code for the solutions is available at github 1 .

A non-Noetherian local ring with finitely generated maximal ideal

Notes

A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.